Ophthalmic lens

ABSTRACT

A progressive multifocal ophthalmic lens has a complex surface having a prism reference point, a fitting cross, a progression meridian having a power addition greater than or equal to 1.5 diopters. The lens has, under conditions when being worn:
         a reduced root mean square, normalized to the addition prescription, of less than 0.65 microns per diopter in a zone delimited by a circle centred on the prism reference point and with a diameter corresponding to a sweep of vision of 80°,   a progression length of less than or equal to 25°, and   a difference in normalized reduced root mean square between pairs of symmetrical points relative to a vertical axis passing through the fitting cross of less than 0.12 microns per diopter in a zone delimited by a semi-circle centred on the fitting cross and with a radius corresponding to raising viewing by 25°.

CROSS REFERENCE TO RELATED APPLICATIONS

Pursuant to U.S.C. § 119, this application claims the benefit of FrenchPatent Application 05 12 063, filed Nov. 29, 2005. The contents of theprior application is incorporated herein by reference in its entirety.

TECHNICAL FIELD

This invention relates to an ophthalmic lens.

BACKGROUND

Any ophthalmic lens intended to be held in a frame involves aprescription. The ophthalmic prescription can include a positive ornegative power prescription as well as an astigmatism prescription.These prescriptions correspond to corrections enabling the wearer of thelenses to correct defects of his vision. A lens is fitted in the framein accordance with the prescription and with the position of thewearer's eyes relative to the frame.

In the simplest cases, the prescription is nothing more than a powerprescription. The lens is said to be unifocal and has a rotationalsymmetry. It is fitted in a simple manner in the frame so that theprincipal viewing direction of the wearer coincides with the axis ofsymmetry of the lens.

For presbyopic wearers, the value of the power correction is differentfor far vision and near vision, due to the difficulties of accommodationin near vision. The prescription thus comprises a far-vision power valueand an addition (or power progression) representing the power incrementbetween far vision and near vision; this comes down to a far-visionpower prescription and a near-vision power prescription. Lenses suitablefor presbyopic wearers are progressive multifocal lenses; these lensesare described for example in FR-A-2 699 294, U.S. Pat. No. 5,270,745 orU.S. Pat. No. 5,272,495, FR-A-2 683 642, FR-A-2 699 294 or also FR-A-2704 327. Progressive multifocal ophthalmic lenses include a far-visionzone, a near-vision zone and an intermediate-vision zone, a principalprogression meridian crossing these three zones. They are generallydetermined by optimization, based on a certain number of constraintsimposed on the different characteristics of the lens. These lenses areall-purpose lenses in that they are adapted to the different needs ofthe wearer at the time.

Families of progressive multifocal lenses are defined, each lens of afamily being characterized by an addition which corresponds to the powervariation between the far-vision zone and the near-vision zone. Moreprecisely, the addition, referenced A, corresponds to the powervariation between a point FV of the far-vision zone and a point NV ofthe near-vision zone, which are respectively called far-vision controlpoint and near-vision control point, and which represent the points ofintersection of viewing with the surface of the lens for far distancevision and for reading vision.

In one family of lenses the addition varies from one lens to the otherin the family between a minimum addition value and a maximum additionvalue of 0.25 diopter and by 0.25 diopter from one lens to the other inthe family.

Lenses with the same addition differ in the value of the mean sphere ata reference point, also called a base. It is possible to choose forexample to measure the base at the point FV for measuring far vision.Thus the choice of a pair (addition, base) defines a group or set ofaspherical front faces for progressive multifocal lenses. Generally, itis thus possible to define 5 base values and 12 addition values, i.e.sixty front faces. In each of the bases an optimization is carried outfor a given power. Starting from semi-finished lenses, of which only thefront face is formed, this known method makes it possible to preparelenses suited to each wearer, by simple machining of a spherical ortoric rear face.

Progressive multifocal lenses thus usually comprise an aspherical frontface, which is the face away from the person wearing the glasses and arear spherical or toric face directed towards the person wearing theglasses. This spherical or toric face allows the lens to be adapted tothe user's ametropia, so that a progressive multifocal lens is generallydefined only by its aspherical surface. As is well known, an asphericalsurface is generally defined by the altitude of all of its points. Theparameters constituted by the minimum and maximum curvatures at eachpoint are also used, or more commonly their half-sum and theirdifference. This half-sum and this difference multiplied by a factorn−1, n being the refractive index of the lens material, are called meansphere and cylinder.

A progressive multifocal lens can thus be defined, at every point on itscomplex surface, by geometric characteristics including a mean spherevalue and a cylinder value, given by the following formulae.

In a manner known per se, at any point of a complex surface, a meansphere D given by the formula:

$D = {\frac{n - 1}{2}\left( {\frac{1}{R_{1}} + \frac{1}{R_{2}}} \right)}$

is defined, where R₁ and R₂ are the maximum and minimum local radii ofcurvature expressed in meters, and n is the index of the materialconstituting the lens.

A cylinder C, given by the formula:

${C = {\left( {n - 1} \right){{\frac{1}{R_{1}} - \frac{1}{R_{2}}}}}},$

is thus defined.

The characteristics of the complex face of the lens can be expressedusing the mean sphere and the cylinder.

Moreover, a progressive multifocal lens can also be defined by opticalcharacteristics taking into account the situation of the wearer of thelenses. In fact, the laws of the optics of ray tracings mean thatoptical defects appear when the rays deviate from the central axis ofany lens. Conventionally, the aberrations known as power defects andastigmatism defects are considered. These optical aberrations can begenerically called obliquity defects of rays.

Obliquity defects of rays have already been clearly identified in theprior art and improvements have been proposed. For example, the documentWO-A-98 12590 describes a method for determination by optimization of aset of progressive multifocal ophthalmic lenses. This document proposesdefining the set of lenses in consideration of the opticalcharacteristics of the lenses and in particular the wearer power andoblique astigmatism under wearing conditions. The lens is optimized byray tracing, using an ergorama linking a target object point with eachdirection of viewing under wearing conditions.

EP-A-0 990 939 also proposes to determine a lens by optimization takinginto account the optical characteristics instead of the surfacecharacteristics of the lens. For this purpose the characteristics of anaverage wearer are considered, in particular as regards the position ofthe lens in front of the eye of the wearer in terms of curving contour,pantoscopic angle and lens-eye distance.

It is thus possible to consider, in addition to the obliquity defects ofrays described previously, the so-called higher order optical aberrationsuch as spherical aberrations or coma by studying the deformations whichare undergone by a non-aberrant spherical wave front passing through thelens.

It is considered that the eye rotates behind the lens in order to sweepover all of its surface. Thus, at each point, an optical system composedof the eye and the lens is considered, as will be explained in detailbelow with reference to FIGS. 1 to 3. The optical system is thereforedifferent at each point of the surface of the lens because the relativepositions of the principle axis of the eye and of the lens are in factdifferent at each point due to the rotation of the eye behind the lens.

In each of these successive positions, the aberrations undergone by thewave front which passes through the lens and is limited by the pupil ofthe eye are calculated.

The spherical aberration results for example from the fact that the rayswhich pass at the edge of the pupil do not converge in the same plane asthe rays which pass close to its centre. Moreover, the coma representsthe fact that the image of a point situated outside the axis has a tail,due to the power variation of the optical system. Reference can be madeto the article by R. G. Dorsch and P. Baumbach, “Coma and DesignCharacteristics of Progressive Addition Lenses” R. G. Dorsch, P.Baumbach, Vision Science and Its Applications, Santa Fe, February 1998which describes the effects of coma on a progressive multifocal lens.

SUMMARY

The deformations of the wave front passing through the multifocal lenscan be described in a global manner by the root mean square or RMS. TheRMS is generally expressed in microns (μm) and, for each point on thecomplex surface, indicates the difference in the resulting wave frontrelative to a non-aberrant wave front. The invention proposescontrolling the RMS value in order to determine a progressive multifocallens defined by its optical characteristics under wearing conditions inorder to limit the optical aberrations perceived by the eye.

In particular when the progressive multifocal lens has a large poweraddition, for example greater than or equal to 1.5 diopters, theaberrations affecting the wave front become more significant due to thepower progression between the far-vision zone and the near-vision zone.These optical aberrations perceived by the wearer adversely affect thecomfort in peripheral vision and in dynamic vision. A need thereforeexists for a progressive multifocal lens which better satisfies theneeds of wearers.

The invention proposes a progressive multifocal lens which is easier toadapt to than the standard ophthalmic lenses; it has a very smooth powerprogression in order to provide the wearer with excellent perception indynamic vision and in peripheral vision. It is proposed to limit the RMSover the whole of a central zone of the lens while guaranteeing goodaccessibility to the powers required in near vision. Such a lens isparticularly suitable for the comfort of hypermetropic wearers whorequire a large power addition, greater than or equal to 1.5 diopters.

Consequently, the invention proposes a progressive multifocal ophthalmiclens with a complex surface having:

a prism reference point;

a fitting cross situated 8° above the prism reference point;

a substantially umbilical progression meridian having a power additiongreater than or equal to 1.5 diopters between a far-vision referencepoint and a near-vision reference point;

the lens having, under wearing conditions and with reference to a planeprescription in far vision by adjustment of the radii of curvature of atleast one of its faces:

a reduced root mean square, normalized to the addition prescription, ofless than 0.65 microns per diopter, in a zone delimited by a circlecentred on the prism reference point and with a diameter correspondingto a sweep of vision of 80°, the reduced root mean square beingcalculated by cancelling the coefficients of the order of 1 and thecoefficient of the order of 2 corresponding to the defocusing in thedecomposition into Zernicke polynomials of a wave front passing throughthe lens;

-   -   a progression length less than or equal to 25°, the progression        length being defined as the angle of lowered vision from the        fitting cross to the point on the meridian at which the wearer's        optical power reaches 85% of the addition prescription;    -   a normalized reduced root mean square difference of less than        0.12 microns per diopter calculated in absolute values as the        difference in root mean square values between pairs of        symmetrical points relative to a vertical axis passing through        the fitting cross, in a zone which includes the far-vision        control point and delimited by a semi-circle centred on the        fitting cross and with a radius corresponding to a raised        viewing of 25°.

According to one characteristic, the root mean square difference betweentwo symmetrical points in said semi-circle is less than or equal to 0.12microns per diopter below a substantially horizontal line situated 8°above the fitting cross.

According to one characteristic, the semi-circle has a base which issubstantially horizontal passing through the fitting cross.

According to one characteristic, the axis of symmetry of the semi-circlesubstantially coincides with the progression meridian.

The invention also relates to a visual device including at least onelens according to the invention and a method for correcting the visionof a presbyopic subject, which comprises providing the subject with, orthe wearing by the subject of, such a device.

DESCRIPTION OF DRAWINGS

Other advantages and characteristics of the invention will becomeapparent on reading the following description of the embodiments of theinvention, given by way of example and with reference to the drawingswhich show:

FIG. 1, a diagram of an eye-lens optical system, top view;

FIGS. 2 and 3, perspective diagrams of an eye-lens system;

FIG. 4, a graph showing the wearer's optical power along the meridian ofa lens according to a first embodiment of the invention;

FIG. 5, a map of the wearer's optical power for the lens of FIG. 4;

FIG. 6, an oblique astigmatism amplitude map of the lens of FIG. 4;

FIG. 7, a map of normalized reduced RMS of the lens of FIG. 4;

FIG. 8, a map representing the differences in RMS between pairs ofsymmetrical points of the lens of FIG. 7;

FIG. 9, a graph showing the wearer's optical power along the meridian ofa lens according to a second embodiment of the invention;

FIG. 10, a map of the wearer's optical power for the lens of FIG. 9;

FIG. 11, an oblique astigmatism amplitude map of the lens of FIG. 9;

FIG. 12, a map of normalized reduced RMS of the lens of FIG. 9;

FIG. 13, a map representing the differences in RMS between pairs ofsymmetrical points of the lens of FIG. 12;

FIG. 14, a graph showing the wearer's optical power along the meridianof a lens according to a prior art;

FIG. 15, a map of the wearer's optical power for the lens of FIG. 14;

FIG. 16, an oblique astigmatism amplitude map of the lens of FIG. 14;

FIG. 17, a map of normalized reduced RMS of the lens of FIG. 14.

DETAILED DESCRIPTION

In a conventional manner, for a given lens, characteristic opticalvariables are defined, namely a power and an astigmatism, underconditions when being worn. FIG. 1 shows a diagram of an eye-and-lensoptical system in a side view, and shows the definitions used hereafterin the description. The centre of rotation of the eye is called Q′; theaxis Q′F′ represented in the figure by a chain-dotted line is thehorizontal axis passing through the centre of rotation of the eye andcontinuing in front of the wearer—in other words the axis Q′F′corresponds to the primary viewing direction. This axis cuts, on thefront face, a point on the lens called the fitting cross FC, which ismarked on the lenses in order to allow their positioning by an optician.The fitting cross is generally situated 4 mm above the geometricalcentre of the front face. Let point O be the point of intersection ofthe rear face and this axis Q′F′. A sphere of the vertices is defined,with a centre Q′, and a radius q′, which cuts the rear face of the lensat the point O. By way of example, a radius q′ value of 27 mmcorresponds to a current value and produces satisfactory results whenthe lenses are worn. The section of the lens can be drawn in the plane(O, x, y) which is defined with reference to FIG. 2. The tangent to thiscurve at the point O is inclined relative to the axis (O, y) at an anglecalled the pantoscopic angle. The value of the pantoscopic angle iscurrently 8°. The section of the lens can also be drawn in the plane (O,x, z). The tangent to this curve at the point O is inclined relative tothe axis (O, z) at an angle called the curving contour. The value of thecurving contour is currently 0°.

A given viewing direction—represented by a solid line in FIG.1—corresponds to a position of the eye in rotation about Q′ and to apoint J on the sphere of the vertices; a viewing direction can also bemarked, in spherical coordinates, by two angles α and β. The angle α isthe angle formed between the axis Q′F′ and the projection of thestraight line Q′J over the horizontal plane containing the axis Q′F′;this angle appears in the diagram of FIG. 1. The angle β0 is the angleformed between the axis Q′F′ and the projection of the straight line Q′Jover the vertical plane containing the axis Q′F′. A given viewingdirection therefore corresponds to a point J of the sphere of thevertices or to a pair (α,β).

In a given viewing direction, the image of a point M in the object spacesituated at a given object distance forms between two points S and Tcorresponding to minimum and maximum distances JS and JT (which aresagittal and tangential focal distances in the case of revolutionsurfaces, and of a point M at infinity) The angle γ marked as the axisof astigmatism is the angle formed by the image corresponding to thesmallest distance with the axis (z_(m)), in the plane (z_(m),y_(m))defined with reference to FIGS. 2 and 3. The angle y is measured incounterclockwise direction when looking at the wearer. In the example ofFIG. 1, on the axis Q′F′, the image of a point of the object space atinfinity forms at the point F′; the points S and T coincide, which isanother way of saying that the lens is locally spherical in the primaryviewing direction. The distance D is the rear front end of the lens.

FIGS. 2 and 3 show perspective diagrams of an eye-lens system. FIG. 2shows the position of the eye and of the reference frame linked to theeye, in the principal viewing direction, α=β=0, called the primaryviewing direction. The points J and O thus coincide. FIG. 3 shows theposition of the eye and of the reference frame which is linked to it inone direction (α,β). In FIGS. 2 and 3 a fixed reference frame {x, y, z}and a reference frame {x_(m),y_(m),z_(m)} linked to the eye arerepresented, in order to show the rotation of the eye clearly. Theorigin of the reference frame {x, y, z} is the point Q′; the axis x isthe axis Q′F′—the point F′ is not represented in FIGS. 2 and 3 andpasses through the point O; this axis is orientated from the lenstowards the eye, in agreement with the direction of measurement of theaxis of astigmatism. The plane {y, z} is the vertical plane; the y axisis vertical and orientated upwards; the z axis is horizontal, thereference frame being directly orthonormalized. The reference frame{x_(m) y_(m), z_(m)} linked to the eye has the point Q′ as its centre;the axis x_(m) is given by the direction JQ′ of viewing, and coincideswith the reference frame {x, y, z} for the primary direction of viewing.Listing's law gives the relationships between the coordinate systems {x,y, z} and {x_(m), y_(m), z_(m)}, for each direction of viewing, seeLegrand, Optique Physiologique, Volume 1, Edition de la Revue d'Optique,Paris 1965.

Using these data, an optical power of the wearer and an astigmatism canbe defined in each viewing direction. For a viewing direction (α,β), anobject point M at an object distance given by the ergorama isconsidered. The points S and T between which the image of the objectforms are determined. The image proximity IP is then given by

${IP} = {\frac{1}{2}\left( {\frac{1}{JT} + \frac{1}{JS}} \right)}$

while the object proximity OP is given by

${OP} = \frac{1}{MJ}$

The power is defined as the sum of the object and image proximities,i.e.

$P = {{{OP} + {IP}} = {\frac{1}{MJ} + {\frac{1}{2}\left( {\frac{1}{JT} + \frac{1}{JS}} \right)}}}$

The amplitude of the astigmatism is given by

$A = {{\frac{1}{JT} - \frac{1}{JS}}}$

The angle of the astigmatism is the angle γ defined above: it is theangle measured in a reference frame linked to the eye, relative to thedirection z_(m), with which the image T forms, in the plane(z_(m),y_(m)). These definitions of power and of astigmatism are opticaldefinitions, under wearing conditions and in a reference frame linked tothe eye. Qualitatively, the thus-defined power and astigmatismcorrespond to the characteristics of a thin lens, which, fitted insteadof the lens in the viewing direction, provides the same images locally.It is noted that, in the primary viewing direction, the definitionprovides the standard value of the astigmatism prescription. Such aprescription is produced by the ophthalmologist, in far vision, in theform of a pair formed by an axis value (in degrees) and an amplitudevalue (in diopters).

The thus-defined power and astigmatism can be experimentally measured onthe lens using a frontofocometer; they can also be calculated by raytracing under wearing conditions.

The invention proposes to consider not only the standard aberrations ofthe wave front, namely the power and the astigmatism, but to take intoaccount all of the higher order aberrations which affect the wave front.

The invention thus proposes a progressive multifocal ophthalmic lenshaving the advantages of an excellent perception in dynamic vision andin peripheral vision while limiting the optical aberrations in a centralzone of the lens covering the far-vision zone, the near-vision zone andthe intermediate-vision zone. The proposed solution also provides a goodaccessibility to the powers required in near vision, allowing the wearerto see satisfactorily at distances equal to approximately 40 cm withoutobliging him to lower his eyes very much, the near-vision zone beingaccessible from 25° below the fitting cross. The lens has a prescriptionsuch that the powers prescribed for the wearer in far vision and in nearvision are achieved on the lens. The proposed lens is particularlysuited to hypermetropic wearers, but it may also be intended for myopicor emmetropic wearers. In each of the figures below, the case of nilpower in far vision is considered, which corresponds to emmetropicwearers.

The lens according to the invention is described below with reference totwo embodiments and compared with a lens of the prior art which does notsatisfy the criteria of the invention (FIGS. 14 to 17).

The lens of FIGS. 4 to 8 is suited to presbyopic wearers having a powerprogression prescription of 2 diopters.

FIGS. 4 to 8 show a lens of diameter 60 mm with a progressive multifocalfront face and comprising a prism of 1.15° with a geometric baseorientated at 270° in the TABO reference. The plane of the lens isinclined 8° relative to the vertical and the lens has a thickness of 3mm A value of q′ of 27 mm (as defined with reference to FIG. 1) wasconsidered for the measurements on the lens of FIGS. 4 to 8.

In FIGS. 5 to 8, the lens is represented in a system with sphericalcoordinates, the beta angle being plotted on the abscissa and the alphaangle on the ordinates.

The lens has a substantially umbilical line, called a meridian, on whichthe astigmatism is practically nil. The meridian coincides with thevertical axis in the upper part of the lens and has an inclination onthe nasal side in the lower part of the lens, the convergence being moremarked in near vision. In the lenses of the applicant, the meridianrepresents the line of intersection of the viewing and the lens when thewearer looks ahead from a point in the far distance to a target point innear vision.

The figures show the meridian as well as reference points on the lens.The fitting cross FC of the lens can be geometrically marked on the lensby a cross or any other mark such as a point surrounded by a circleproduced on the lens, or by any other appropriate means; this is acentring point produced on the lens which is used by the optician to fitthe lens in the frame. In spherical coordinates, the fitting cross FChas the coordinates (0,0) as it corresponds to the point of intersectionof the front face of the lens and the primary viewing direction, asdefined previously. The far-vision control point FV is situated on themeridian and corresponds to a raised viewing of 8° above the fittingcross; the far-vision control point FV has the coordinates)(0,−8°) inthe predefined spherical reference. The near-vision control point NV issituated on the meridian and corresponds to a lowered viewing of 35°below the fitting cross; the near-vision control point NV has thecoordinates (6°,35°) in the predefined spherical coordinate system.

A lens also has a prism reference point PRP corresponding to thegeometrical centre of the lens. On the lens of the applicant, thefitting cross FC is situated 8° above the prism reference point; or, inthe case of a surface characterization of the lens, 4 mm above thegeometrical centre (0,0) of the lens.

FIG. 4 shows a graph of the optical power of the wearer along themeridian; the angle β is plotted on the ordinates and the power on theabscissa in diopters. The minimum and maximum optical powerscorresponding respectively to the quantities 1/JT and 1/JS definedpreviously are shown by dotted lines, and the optical power P by a solidline.

It is then possible to note in FIG. 4 an optical power of the wearerwhich is substantially constant around the far-vision control point FV,an optical power of the wearer which is substantially constant aroundthe near-vision control point NV and a regular progression of the poweralong the meridian. The values are shifted to zero at the origin wherethe optical power is actually −0.05 diopters corresponding to a lensprescribed for presbyopic emmetropic wearers.

The intermediate-vision zone generally begins, for a progressivemultifocal lens, at the fitting cross FC; it is here that the powerprogression begins. Thus the optical power increases, from the fittingcross to the near-vision control point NV, for values of the angle β of0 to 35°. For angle values beyond 35°, the optical power becomessubstantially constant again, with a value of 2.11 diopters. It is notedthat the progression of optical power of the wearer (2.17 diopters) isgreater than the prescribed power addition A (2 diopters). Thisdifference in power value is due to the oblique effects.

It is possible to define on a lens a progression length PL which is theangular distance—or the difference in ordinates—between the fittingcross FC and a point on the meridian at which the power progressionreaches 85% of the prescribed power addition A. In the example of FIG.4, a progression of optical power of 0.85×2 diopters, i.e. 1.7 diopters,is obtained for a coordinate point of angle β=approximately 24.5°.

The lens according to the invention thus has a good accessibility to thepowers required in near vision with a moderate lowered vision, less thanor equal to 25°. This accessibility guarantees comfortable use of thenear-vision zone.

FIG. 5 shows the contour lines of the optical power of the wearerdefined in a direction of viewing and for an object point. As is usual,the isopower lines have been plotted in FIG. 5 in a spherical coordinatesystem; these lines are formed by the points having the same value ofoptical power P. The 0 diopter to 2 diopter isopower lines arerepresented.

FIG. 6 shows the contour lines for the amplitude of the obliqueastigmatism under conditions when being worn. As is usual, theisoastigmatism lines have been plotted in FIG. 6 in a sphericalcoordinate system; these lines are formed by the points having the sameastigmatism amplitude value as defined previously. The 0.25 diopter to1.75 diopter isoastigmatism lines are represented.

FIG. 7 shows the contour lines for the normalized reduced RMS calculatedunder conditions when being worn. The RMS is calculated for each viewingdirection and thus for each point on the glass of the lens, with a raytracing method. Initially, for each viewing direction and therefore eachpoint of the lens, the wave front is calculated after having passedthrough the lens and the wearer's prescription—power, axis and amplitudeof astigmatism—is subtracted from it in a vectorial manner in order todetermine the resulting wave front. A diameter of the wearer's pupilapproximately equal to 5 mm was considered. The RMS represents, for eachpoint of the lens corresponding to a viewing direction, the differencebetween the resulting wave front and a non-aberrant spherical referencewave front corresponding to the desired power for the viewing directionlinked to this point of the lens. The RMS values shown in FIG. 7 werecalculated for the lens of FIGS. 4 to 6, i.e. for a lens with planepower in far vision and having a prescription for 2 diopter poweraddition, prescribed for presbyopic emmetropic wearers.

A possible fitting in order to measure the aberrations of a wave frontpassing through the lens as perceived by the eye of the wearer isdescribed in the article by Eloy A. Villegas and Pablo Artal, “SpatiallyResolved Wavefront Aberrations of Ophthalmic Progressive-Power Lenses inNormal Viewing Conditions”, Optometry and Vision Science, Vol. 80, No.2, February 2003.

In a known manner, a wave front which has passed through an asphericalsurface can be decomposed by Zernicke polynomials. More precisely, awave surface can be approximated by a linear combination of polynomialsof the type:z(x, y, z)=Σ_(i)a_(i)p_(i) 9x, y, z)

where the P_(i) are Zernicke polynomials and the a_(i) are realcoefficients.

The decomposition of the wave front into Zernicke polynomials and thecalculation of the aberrations of the wave front were standardized bythe Optical Society of America; the standard being available on the website of Harvard Universityftp://color.eri.harvard.edu/standardization/Standards TOPS4.pdf.

The RMS is calculated in this way, under wearing conditions. The RMS isthen reduced, i.e. the coefficients of order 1—which correspond to theprismatic effects—and the coefficient of order 2 corresponding to thedefocusing in the decomposition of the wave front into Zemicke Zernickepolynomials are cancelled. The optical aberrations caused by powerdefects are therefore not included in the calculation of reduced RMS; onthe other hand the coefficients of order 2 corresponding to the residualastigmatism of the lens are retained. The RMS is then normalized, i.e.divided by the prescribed power addition.

In FIG. 7, the normalized reduced RMS, expressed in microns per diopter,is represented. The 0.1 μm/D to 0.5 μm/D iso RMS lines are represented.In FIG. 7 a circle is also marked out centred on the prism referencepoint—i.e. the geometrical centre of the lens before trimming andpositioning in a frame. In spherical coordinates, the prism referencepoint PRP has the coordinates (0,−8°) because it is situated 8° or 4 mmbelow the fitting cross FC. This circle also has a diametercorresponding to a sweep of vision of 80°—i.e. of approximately 40 mmdiameter if a surface characterization of the complex surface of thelens is considered. In the zone of the lens covered by this circle,which includes the far-vision control point FV, the near-vision controlpoint NV and consequently all of the intermediate-vision zone, thenormalized reduced RMS is limited to 0.65 μm/D. Imposing a small RMSvalue over all of this central zone of the lens provides the wearer withoptimal comfort of visual perception in peripheral vision and in dynamicvision.

In FIG. 8, contour lines representing the difference in normalizedreduced RMS values between symmetrical points relative to a verticalaxis passing through the fitting cross FC are represented. The map ofFIG. 8 is constructed point by point by considering all the pairs ofsymmetrical points on either side of the predefined vertical axis and bycalculating the difference in normalized reduced RMS between these twopoints. The absolute value of this difference is then shown on the mapof FIG. 8. It is noted that all the normalized reduced RMS isodifferencelines are symmetrical relative to this vertical axis passing through thefitting cross FC.

A semi-circle centred on the fitting cross FC and including thefar-vision control point is also marked out in FIG. 8. This semi-circlehas a radius corresponding to a raised viewing of 25°—i.e. ofapproximately 12.5 mm radius if a surface characterization of thecomplex surface of the lens is considered. This semi-circle can have asubstantially horizontal base passing through the fitting cross; thebase can however be inclined according to the methods of fitting thelens in a frame which depend on the lens manufacturers. The semi-circledefined above must include the far-vision control point FV and thehorizontal zone of the lens which is used most often in far vision.

In the zone delimited by this semi-circle, the difference in normalizedreduced RMS on either side of the axis of symmetry is less than 0.12microns per diopter.

The lens according to the invention also has a small difference innormalized reduced RMS between the temporal and nasal parts of the farvision zone. This characteristic ensures optimal wearer comfort in farvision. In fact, when the wearer looks into the distance by shifting hiseyes slightly horizontally, he looks through the nasal part of a lenswith one eye and through the temporal part of the other lens with theother eye. For good binocular balance it is important that theperspective qualities are substantially the same for both eyes, i.e.that the optical aberrations perceived by each eye are substantially thesame. By guaranteeing normalized reduced RMS values which aresubstantially symmetrical on either side of a vertical axis in farvision it is ensured that the wearer's left eye and right eye encountersubstantially the same optical defects, which ensures a good balance ofperception between the two eyes.

A substantially horizontal line situated 8° above the fitting cross—i.e.approximately 4 mm above the fitting cross in surface characterizationof the lens, is also marked out in FIG. 8. For the lenses of theapplicant, this horizontal line therefore passes beneath the far-visioncontrol point as has been defined previously.

In said semi-circle and beneath said horizontal line, the difference innormalized reduced RMS between the nasal and temporal zones is less than0.12 microns per diopter. This very small difference in normalizedreduced RMS value allows optimal comfort in binocular vision because itis this horizontal zone just above the fitting cross which is most usedby a wearer when he looks at a point in far vision while moving his eyeslaterally behind his lenses.

In FIG. 8 it is seen that the vertical axis of symmetry between thenasal and temporal parts of the lens substantially coincides with theprogression meridian in far vision. In fact, in the lenses of theapplicant, the progression meridian is defined as the line of visionwithout lateral movements of the eyes from a target point in far visionto a target point in near vision. It is understood that otherdefinitions can be envisaged for the progression meridian and that thevertical axis of symmetry cannot then coincide with the meridian as isthe case in FIG. 8.

The lens of FIGS. 9 to 13 is another example of a lens according to theinvention; the lens of FIGS. 9 to 13 is suitable for presbyopic wearershaving a prescription for a 2.5 diopter power progression.

FIGS. 9 to 13 show a lens of diameter 60 mm with a progressivemultifocal front face and comprising a prism of 1.44° with a geometricbase orientated at 270° in the TABO reference. The plane of the lens isinclined 8° relative to the vertical and the lens has a thickness of 3mm A value of q′ of 27 mm (as defined with reference to FIG. 1) wasconsidered for the measurements on the lens of FIGS. 9 to 13.

FIG. 9 shows a graph of the optical power of the wearer along themeridian. The values are shifted to zero at the origin, where theoptical power is actually −0.06 diopters corresponding to a plane lensin far vision prescribed for presbyopic emmetropic wearers.

As in FIG. 4, a progression length PL is defined which is the angulardistance—or the difference in ordinates—between the fitting cross FC—anda point on the meridian at which the power progression reaches 85% ofthe prescribed power addition A. In the example of FIG. 9, an opticalpower progression of 0.85×2.5 diopters, i.e. 2.125 diopters, is obtainedfor a coordinate point of angle β=approximately 24.50. The lensaccording to the invention thus has a good accessibility to the powersrequired in near vision with a moderate lowering of viewing, less thanor equal to 25°. This accessibility guarantees comfortable use of thenear-vision zone.

FIG. 10 shows the contour lines for the optical power of the wearerdefined in a viewing direction and for an object point. In FIG. 10, the0 diopter to 2.50 diopter isopower lines are plotted in a reference withspherical coordinates.

FIG. 11 shows the contour lines for the amplitude of the obliqueastigmatism under wearing conditions. In FIG. 11, the 0.25 diopter to2.25 diopter isoastigmatism lines are plotted in a reference withspherical coordinates.

FIGS. 12 and 13 are similar to FIGS. 7 and 8 described above. It isnoted in FIGS. 12 and 13 that the values of normalized reduced RMS andof difference in normalized reduced RMS between nasal and temporal zonesdepend only to a small extent on the prescribed addition value.

The lens of FIGS. 14 to 17 is an example of a lens of the prior art,marketed by Essilor under the name Varilux Comfort®. The lens of FIGS.14 to 17 is suitable for presbyopic emmetropic wearers having aprescription for a 2 diopter power progression.

FIG. 17 shows the normalized reduced RMS iso lines. It is noted in FIG.17 that the normalized reduced RMS exceeds the value of 0.65 microns perdiopter in the central zone of the lens.

A smooth and regular variation in the power between the far-vision zoneand the near-vision zone compared with FIG. 15 is also noted in FIGS. 5and 10. This smooth variation makes it possible to limit the opticalaberrations, in particular astigmatism, in order to maintain anormalized reduced RMS which is not very great over all of the centralzone of the lens as shown in FIGS. 7 and 12 compared with the lens ofFIG. 17.

A regular and symmetrical distribution of the isoastigmatism lines oneither side of the meridian as well as lower levels of astigmatismcompared with FIG. 16 are also seen in FIGS. 6 and 11. Thesecharacteristics of the astigmatism make it possible to limit the opticalaberrations and to maintain a normalized reduced RMS which is not verygreat over all of the central zone of the lens, compared with the lensof FIG. 17.

The lens according to the invention is prescribed by considering theprescriptions of the wearer in far vision and in near vision whichdetermines the necessary addition. When the complex surface is on thefront face of the lens, the necessary power can be obtained, as in thestate of the art, by machining the rear face in order to ensure that thepower is identical to the prescribed power.

The fitting of the lens in a visual device can take place in thefollowing manner. The horizontal position of the wearer's pupil in farvision is measured, i.e. the interpupillary half-distance only, and theoverall height of the dimensions of the frame of the visual device isdetermined. The lens is then fitted in the visual device with thefitting cross positioned in the measured position.

In this regard reference can be made to the patent application FR-A-2807 169 describing a simplified method for fitting ophthalmic lenses ina frame. This document in particular describes the differentmeasurements made by opticians and proposes to measure only theinterpupillary half-distance in order to carry out the fitting of thelenses in the frame using the overall height of the dimensions of theframe.

The fitting of the lens therefore only requires a standard measurementof the interpupillary half-distance for far vision as well as ameasurement of the height of the dimensions of the frame in order todetermine the height at which the fitting cross must be placed in theframe. The lens is then cut out and fitted in the frame in such a waythat the fitting cross is situated in a determined position. Thedetermination of the vertical position of the fitting cross can ofcourse be carried out in a standard manner through measurement of thefitting height by measuring the position in the frame of the subject'svision in far vision; this measurement takes place in a standard manner,the subject wearing the frame and looking into the far distance.

The lens according to the invention allows improved tolerance for thefitting described above. This tolerance is provided by limiting theoptical aberrations around the fitting cross. In particular thenormalized reduced RMS value and the differences in normalized reducedRMS symmetry are limited around the fitting cross.

The lens described above can be obtained by optimization of a surfaceaccording to the optimization methods known per se and described in theabove-mentioned documents of the state of the art relating toprogressive multifocal lenses. In particular optimization software isused in order to calculate the optical characteristics of the lens-eyesystem with a predetermined merit function. For the optimization, one ormore of the criteria set out in the above description can be used, andin particular:

a reduced RMS normalized to the addition prescription of less than 0.65microns per diopter, in a zone delimited by a circle centred on theprism reference point PRP and with a diameter corresponding to a sweepof vision of 80°.

a progression length less than or equal to 25°,

a difference in normalized reduced RMS of less than 0.12 microns perdiopter, calculated in absolute values as the difference in normalizedreduced RMS values between pairs of symmetrical points relative to avertical axis passing through the fitting cross, in a zone including thefar-vision control point FV and delimited by a semi-circle centred onthe fitting cross FC and with a radius corresponding to raising viewingby 25°.

These criteria can be combined with others and in particular with adifference in normalized reduced RMS of less than or equal to 0.12microns per diopter below a substantially horizontal line situated 8°above the fitting cross.

The choice of these criteria makes it possible to obtain a lens byoptimization. A person skilled in the art readily understands that thelens in question does not necessarily have values corresponding exactlyto the set criteria; for example, it is not essential for the uppervalue of the normalized reduced RMS to be obtained.

In the above examples of optimization it is proposed to optimize onlyone of the faces of the lenses. It is clear that in all of theseexamples, the roles of the front and rear surfaces can easily beswitched once optical targets similar to those of the lens described areobtained.

1. Progressive multifocal ophthalmic lens with a complex surface having:a prism reference point; a fitting crosssituated 8° above the prismreference point; a substantially umbilical progression meridian having apower addition greater than or equal to 1.5 diopters between afar-vision reference point and a near-vision reference point; the lenshaving, under wearing conditions and with reference to a planeprescription in far vision by adjustment of the radii of curvature of atleast one of its faces: a reduced root mean square, normalized to theaddition prescription, of less than 0.65 microns per diopter, in a zonedelimited by a circle centred centered on the prism reference a pointlocated 8° below the fitting cross and with a diameter corresponding toa sweep of vision of 80°, the reduced root mean square being calculatedby cancelling the coefficients of order 1 and the coefficient of order 2corresponding to the defocusing in the decomposition into ZemickeZernicke polynomials of a wave front passing through the lens; aprogression length less than or equal to 25°, the progression lengthbeing defined as the angle of lowered viewing from the fitting cross tothe point of the meridian at which the wearer's optical power reaches85% of the addition prescription; a normalized reduced root mean squaredifference of less than 0.12 microns per diopter calculated in absolutevalues as the difference in root mean square values between pairs ofsymmetrical points relative to a vertical axis passing through thefitting cross, in a zone which includes the far-vision control point anddelimited by a semi-circle centred on the fitting cross and with aradius corresponding to a raised viewing of 25°.
 2. The lens of claim 1,characterized in that said root mean square difference between twosymmetrical points in said semi-circle is less than or equal to 0.12microns per diopter below a substantially horizontal line situated 8°above the fitting cross.
 3. The lens of claim 1, characterized in thatthe semi-circle has a substantially horizontal base passing through thefitting cross.
 4. The lens of claim 1, characterized in that the axis ofsymmetry of the semi-circle substantially coincides with the progressionmeridian.
 5. A visual device including at least one progressivemultifocal ophthalmic lens with a complex surface having: a prismreference point; a fitting crosssituated 8° above the prism referencepoint; a substantially umbilical progression meridian having a poweraddition greater than or equal to 1.5 diopters between a far-visionreference point and a near-vision reference point; the lens having,under wearing conditions and with reference to a plane prescription infar vision by adjustment of the radii of curvature of at least one ofits faces: a reduced root mean square, normalized to the additionprescription, of less than 0.65 microns per diopter, in a zone delimitedby a circle centered on the prism reference a point located 8° below thefitting cross and with a diameter corresponding to a sweep of vision of80°, the reduced root mean square being calculated by cancelling thecoefficients of order 1 and the coefficient of order 2 corresponding tothe defocusing in the decomposition into Zernicke polynomials of a wavefront passing through the lens; a progression length less than or equalto 25°, the progression length being defined as the angle of loweredviewing from the fitting cross to the point of the meridian at which thewearer's optical power reaches 85% of the addition prescription; anormalized reduced root mean square difference of less than 0.12 micronsper diopter calculated in absolute values as the difference in root meansquare values between pairs of symmetrical points relative to a verticalaxis passing through the fitting cross, in a zone which includes thefar-vision control point and delimited by a semi-circle centred on thefitting cross and with a radius corresponding to a raised viewing of25°.
 6. A method for correcting the vision of a presbyopic subject,which comprises providing the subject with, or the wearing by thesubject of, a visual device including at least one progressivemultifocal ophthalmic lens with a complex surface having: a prismreference point, a fitting crosssituated 8° above the prism referencepoint; a substantially umbilical progression meridian having a poweraddition greater than or equal to 1.5 diopters between a far-visionreference point and a near-vision reference point; the lens having,under wearing conditions and with reference to a plane prescription infar vision by adjustment of the radii of curvature of at least one ofits faces: a reduced root mean square, normalized to the additionprescription, of less than 0.65 microns per diopter, in a zone delimitedby a circle centred centered on the prism reference a point located 8°below the fitting cross and with a diameter corresponding to a sweep ofvision of 80°, the reduced root mean square being calculated bycancelling the coefficients of order 1 and the coefficient of order 2corresponding to the defocusing in the decomposition into ZemickeZernicke polynomials of a wave front passing through the lens; aprogression length less than or equal to 25°, the progression lengthbeing defined as the angle of lowered viewing from the fitting cross tothe point of the meridian at which the wearer's optical power reaches85% of the addition prescription; a normalized reduced root mean squaredifference of less than 0.12 microns per diopter calculated in absolutevalues as the difference in root mean square values between pairs ofsymmetrical points relative to a vertical axis passing through thefitting cross, in a zone which includes the far-vision control point anddelimited by a semi-circle centred on the fitting cross and with aradius corresponding to a raised viewing of 25°.
 7. The lens of claim 1,wherein the complex surface has a prism reference point located 8° belowthe fitting cross.
 8. The visual device of claim 5, wherein the complexsurface of the lens has a prism reference point located 8° below thefitting cross.